Recently, in order to realize a power semiconductor device such as a switching device and a high-frequency power semiconductor device, a nitride semiconductor material having high critical field strength is actively researched. JP-A 2006-222414 (KOKAI) discloses a heterojunction field-effect transistor having a recess structure in a gate electrode forming region. A gate insulating film of the transistor is stacked film made of a silicon nitride film and a high-dielectric-constant insulating film. The structure intended to realize normally-off operation and to improve transconductance in a nitride-based semiconductor device.